Problem 22
<h3>Answers:</h3>
- vertical: rectangle
- horizontal: rectangle
- angled: parallelogram
----------
Explanation:
The vertical and horizontal cross sections are fairly straight forward. They are simply mirror images of the outward showing faces. The angled cross sections are a bit more complicated and there's a lengthy proof involved, but long story short, the angled cutting plane divides the 3D solid such that we have 2 sets of lines that have the same slope (if we consider a 2D view), which leads to 2 sets of parallel sides.
==================================================
Problem 23
<h3>Answers:</h3>
- vertical: either a triangle or quadrilateral
- horizontal: triangle
- angled: either a triangle or quadrilateral
----------
Explanation:
The horizontal cross section is always a triangle because the bottom base face is a triangle. The other two types of cross sections are either triangles or quadrilaterals depending on where the cutting plane is situated. For vertical cross sections that go through the apex point, we get a triangle. For vertical cross sections that do not go through the apex, then we get a quadrilateral. Sometimes a trapezoid is possible here, but not always. It's better to just consider it a quadrilateral to be the most general. A similar situation happens with the angled cuts as well.
==================================================
Problem 24
<h3>Answers:</h3>
- vertical: triangle, but only if plane is crossing through apex
- horizontal: circle
- angled: ellipse or parabola
----------
Explanation:
Imagine you shined a flashlight onto the cone such that the flashlight is perfectly level and flat. It would cast a shadow that is a triangle. This is one way to think of a cross section. If you vertically slice. The horizontal cross sections are always circles due to the circular base of the cone. The angled cross sections are either ellipses or parabolas. For more information, look in your math textbook about conic sections (just ignore the second cone however).
==================================================
Problem 25
<h3>Answers:</h3>
- vertical: rectangle
- horizontal: circle
- angled: ellipse
----------
Explanation:
The horizontal cross sections are circles for similar reasoning as the cone horizontal cross section. However, this time the vertical cross sections are rectangles. The widest possible rectangle is the result of the vertical cutting plane passing through the center of the circular base. Angled cross sections are ellipses. Though some portions of the ellipse may be cut off depending on what the actual angle is.
42069 i tend to believe the distortion of this prudential center of a good one and a good thing about the way that it was to be with you and your mom is not really a part you do hw was the way uuuuuuuu
Answer:
<em>Thus the domain is the real numbers and the range is y>3.</em>
<em>Answer: Option C)</em>
Step-by-step explanation:
<u>Domain and Range of Functions</u>
To determine the domain and range of a function given on a graph, we use the vertical and horizontal line methods respectively.
The domain consists of all the values of x for which the function exists. We are told that the function is an exponential decay. Exponential functions without specified restrictions have a domain of all the real numbers.
Imagine a vertical line moving from minus infinite x to plus infinite. The line would always cross the graph at one point, thus the domain is all the real numbers.
Now for the range, imagine a horizontal line coming from y minus infinite. It won't get in contact with the graph until it approaches y=3. Once it goes up y=3, the line touches the graph in one point up to infinity y. The range is y>3.
Thus the domain is the real numbers and the range is y>3.
Answer: Option C)
Answer:
The Answer is D
Step-by-step explanation:
The figure shows blocks sectioned out in thirds. Every 2/3rd portion is colored separately. Here there are 2 blocks, and when divided into 2/3rd, you get 3 possible sections.
Answer:
29.1°
Step-by-step explanation:
Given that :
Riser, AB, Opposite = 10 cm
Thread, = AC, Adjacent = 18 cm
Angle of inclination, θ
Using trigonometry :
Tan θ = opposite / Adjacent = AB / AC
Tan θ = 10 / 18
θ = tan^-1(10/18)
θ = 29.055
Hence, angle of inclination is 29.1° (1 decimal place)